2C+Absolute+Value+Equations,+Circles,+Ellipses,+and+their+graphs

==Absolute Value Equations,Circles, and their graphs==

**Circles**
This is the graphing form of a circle graph. math (x-h)^2-(y-k)^2=r^2 math

This is the standard form of a circle graph. math y=\pm\sqrt{r^2-(x-h)^2}+k math

Here is an example of an equation that will be graphed as a circle. math Graphing Form: (x-4)^2+(y-3)^2=2^2 math

math Standard Form: y=\pm\sqrt{2^2-(x-4)^2}+3 math



To Find the Radius and Vertex from an Equation in Graphing Form

math (x-4)^2+(y-3)^2=2^2 math

When you look at this equation you see x-4, so 'h' has to be 4, then if you look at y-3, 'k' would have to be 3. So the vertex of the circle would be at (4,3). The the radius is 2.

__**Another Example**__

math Graphing Form:(x-3)^2+(y-3)^2=4^2 math

math Standard Form:y=\pm\sqrt{4^2-(x-3)^2}+3 math

Vertex= (h,k)-->(3,3) Radius=(r)-->4

 =**Absolute Value**=

Absolute value is the value at that represents how far away from zero a number is. For example, the absolute value of denoted |x| = 5, x can be 5 or -5, because -5 and 5 are both 5 digits away from 0. The same can be applied with |x| = 10, value of x can be 10 or -10, because -10 and 10 are both 10 digits away from zero.

The formula for an absolute value is f(x) = a(|x-h|)+k

When graphing an absolute value, the graph is always a V.



Key For Moving Absolute Value graphs. Using 1 and 2 as substitutes

Move Up: |x|+1 Down: |x|-1 Stretch: |x|/2 Compress: 2|x| Move Right: |x-1| Move Left: |x+1|